Binomial Theorem

Today we learned about Binomial Expansion. Although it can look quite daunting at first because of how big Pascal's triangle is, it is actually white simple when you break it down. When you write out the coefficients for a binomial that is raised to a power, you are expanding a binomial. There are two methods of expansion, both of which provide binomial coefficients. The first is Binomial Theorem, which states that in the expansion of 

(x + y)^n: (x + y) ^n = x^n + (nx^n-1)y +...+ (n)C(r) (x^n-r)y^r +...+ nxy^n-1 + y^n.The coefficient of (x^n-r)y^r is given by a procedure known as combination: (n)C(r) = n! / (n-r)!r!. 

The second is Pascal's Triangle, in which the first andlast number in each row is 1. Every other number in each row is formed by adding the two numbers immediately above the number. A basic illustration of Pascal's triangle is:

With this triangle, simply use the prior formula and correspond it with the amount of rows or n that is given in the problem.